Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23818 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C22×D4 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C43×C11 ◁ G | |
758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,18)(14,19,15,17)(20,21,23,25)(22,26,27,24)(28,29,32,35)(30,33,38,42)(31,34,39,43)(36,40,37,41);(12,14,16,15)(13,17,18,19)(20,22,23,27)(21,24,25,26)(28,30)(29,33)(31,36)(32,38)(34,40)(35,42)(37,39)(41,43);(21,25)(24,26)(30,36)(31,39)(33,40)(34,43)(37,38)(41,42);(12,15,16,14)(13,17,18,19)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16806);